Mathematical techniques are developed for the analysis of data from the measurement of chemical parameters and for the optimization of such experiments. Work has continued on the development of exact representation of the probability densities that arise in crystallographic analysis. Relevant theory has been developed for such densities in direct methods of phase determination. Numerical techniques have been developed for the analysis of dielectric measurements on certain classes of polymers and proteins. A perturbation theory analysis of nuclear magnetic resonance correlation experiments has been applied to such experiments in the nonlinear regime.